You are using an outdated browser that does not fully support the intranda viewer.
As a result, some pages may not be displayed correctly.

We recommend you use one of the following browsers:

Full text

Mapping without the sun
Zhang, Jixian

a result, the process no longer describes a global birth-and-death
but regional expansions and shrinkages of the sets under study
namely the front, the seats and the scar of the spread. We draw
from the model instructive simulations and a precise predictor of
scars that actually occurred in the State of Selangor during the
period 2000-2004.
For the moment, fire daily predictions were not tested. This will
be a future work to undertake.
Figure 8: Cumulative number of hot spots from 2000 to 2004,
during the periods April-June (a), July-September (b), and
October-December (c).
a) b) c)
The authors would like to thank The Cilix Corp. for having al
lowed them to use their maps of fuel combustion and spread rate.
Abdullah, M.J., M.R. Ibrahim, and A.R. Abdul Rahim : The inci
dence of forest fire in Peninsular Malaysia: History, root causes,
prevention and control. Workshop on prevention and control of
fire in peatland, Kuala Lumpur, Malaysia, 19-21 March 2002.
Figure 9: a) cumulative number of hot spots from 2000 to 2004,
during the period January to March, b) and c) two simulations
based on the input set a) with two values of k in the ratio 1.5.
Selangor area a(S) is equal to 79, 969 pixels, and in the simula
tion of Figure9c, the average number of Poisson points over the
set S of Selangor is 500. On the other hand, the sum of the fuel
amount over S equals 304,130, in dimensionless units. There
fore, by integrating Equation(20) over S, we find numerically
J s 0{x)d(x) = 7 g°g 6g = k f fw{x)d(x)
from which we draw
79,969 k
k = 1.64 x 10~ 3
4.2 Fire spread simulations
If Io stands for the input set, then each point x of Io is replaced
by one of the discs of Figure7, according to the value r(x) of the
spread rate map at point x, which results in 5(x). Then, the simu
lated new seats I\ = /3(/o) are obtained by intersecting each S(x)
by a realization J of Poisson points, as indicated in Relation(2),
with intensity 6 = kf w , and by taking the union for all x of Io-
Finally, each point y of the set of new seats I\ is replaced in turn
by S(y), and the dilation X2 = S(I\), as given by Relation(3),
consists in the union of the discs S(y).
Figure 9b and c depict two propagation simulations <5(/i) when
we take a winter input set Io (Figure 9a), and when we use the
two maps r and / of Figure 2. The two simulations differ by
their coefficients k, which are taken such that kb/ k c = 1.5. The
values chosen for kb amplifies the phenomenon. One will notice
that most of the small hot spots of Figure 9a do not develop fires.
This paper proposes a new Random set model, the random spread.
More than the classical spatial birth-and-death processes, random
spread depends strongly on the heterogeneity of the space, which
appears via two functions of intensity (9) and extension (6). As
ADB (Asian Development Bank) and BAPPENAS (National De
velopment Planning Agency). Causes, extent, impact and costs of
1997/98 fires and drought. Final Report, Annex 1 and 2. Planning
for Fire Prevention and Drought Management Project. Asian De
velopment Bank TA 2999-1NO July 1998 - March 1999. Fortech.
Pusat Pengembangan Agribisnis, Margueles Poyry. Jakarta, In
P. Bak, K. Chen, C. Tang : Phys. Letters A 147, 297. 1990.
P. Bak, K. Chen, M. Paczuski : Solitons in the one-dimensional
forest fire model, Physical Review Letters, The American Physi
cal Society, vol. 86 no. 11, March 2001.
R. Blanchi, M. Jappiot, D. Alexandrian : Forest fire risk assess
ment and cartography. A methodological approach. Forest Fire
Research and Wildland Fire Safety, Viegas Ed. Millpress Rotter
dam, 2002.
M. Bilodeau, F. Meyer and M. Schmitt (Edts) Space, Structure,
and Randomness Lecture Notes in Statistics, Springer, 2005
P. Carrega : Relationship between wind speed and the rate of
spread of a fire front in field conditions : an experimental example
from the Landes forest. Forest Fire Research and Wildland Fire
Safety, Viegas Ed. Millpress Rotterdam, 2002.
W.R. Catchpole, E.A. Catchpole, A.G. Tate, B. Butler, R.C. Rom
mel : A model for the steady spread of fire through a homoge
neous fuel bed. Forest Fire Research and Wildland Fire Safety,
Viegas Ed. Millpress Rotterdam, 2002.
Colin, Colin, P.-Y., and Al., 2002. Saltus program-spot fires:
knowledge and modelling, in Proc.ofthe IV international conf.or
Fire Research, Luso, Portugal, 2002.
FAO An Overview of Forest Products Statistics in South and
Southeast Asia. Information and Analysis for Sustainable For
est Management: Linking National and International Efforts
in South and Southeast Asia (Qiang, M. & J.S. Braodhead.
eds.). Food and Agriculture Organization of the United Nations,
Bangkok. 177 p., 2002.
Fire Detection and Monitoring using Remote Sensing, in
Hotspots Interpretation Manual, Asian Specialized Meteorologi
cal Centre, Singapore intranet, 2003.
Forestry Canada 1
ture of the Canad
Forestry Canada, 1
Gantz, D.: Framin
est and land fires
Union, pp. 92. 20(
M.D. Hairi Sulims
dom Simulations
Chen Ed., AIT Ba
Mastura Mahmud,
East Asia National
12 Nov. 1999, Bar
G. Matheron: Rar
York, 1975.
I. Molchanov, Ran
149, 2005.
C. J. Preston, Spati
46,1977, pp371-3<
J. Serra, Image c
II: theoretical adx
J.Serra, Random S
March 2006.
0. Sero-Guillaum
a complete set of e
modynamics. Int.
pp 1705-1722.
D. Stoyan, W. S. K
its Applications, 2
S. Tahir Qadri Ed.
Strategy Asian De
J.A. Turner, B.D.
Danger Rating Sy
practices. Environ
Victoria, BC, BC-
W. S. Wan Ahmac
pp. 66-74, 2002.
Zhang, Y.-H., Wo
Monthly burned a
for the Russian Fe
Environment, 87,2